Exposure apparatuses are commonly used to transfer images from a reticle onto a semiconductor wafer during semiconductor processing. A typical exposure apparatus includes an illumination source, a reticle stage assembly that retains a reticle, an optical assembly, a wafer stage assembly that retains a semiconductor wafer, a measurement system, and a control system.
In one embodiment, the wafer stage assembly includes a wafer stage that retains the wafer, and a wafer mover assembly that precisely positions the wafer stage and the wafer. Somewhat similarly, the reticle stage assembly includes a reticle stage that retains the reticle, and a reticle mover assembly that precisely positions the reticle stage and the reticle.
The size of the images and features within the images transferred onto the wafer from the reticle are extremely small. Accordingly, the precise positioning of the wafer and the reticle relative to the optical assembly is critical to the manufacture of high density, semiconductor wafers.
Recently, E/I core type actuator pairs have been used in the wafer stage assembly and/or the reticle stage assembly. E/I core type actuator pairs can include a pair of generally “E” shaped electromagnets and a pair of “I” shaped targets that are positioned between the two electromagnets. Each electromagnet has an electrical coil wound around the center section. Current directed through the coils creates an electromagnetic field that attracts the target toward the electromagnet. The amount of current determines the amount of attraction. By making the current through one coil of the pair to be larger than the current through the other coil in the pair, a differential force can be produced to draw the target in one direction or its opposing direction. This resultant force can be used to move a stage or other device. For, example, for an exposure apparatus, the control system can direct current to the electromagnets to control the position of the stage.
Each electromagnet and target is separated by an air gap g that is very small. Currently, some system designers use the following formula to calculate the attractive force between the electromagnet and the target:F=K(i/g)2
Where F is the attractive force, measured in Newtons; K is an electromagnetic constant which is dependent upon the geometries of the E-shaped electromagnet, I-shaped target and number of conductor turns about the magnet; i is the current, measured in amperes; and g is the gap distance, measured in meters.
Application of the above equation presumes that the “E” shaped electromagnets and the “I” shaped targets are manufactured and aligned to exacting specifications. When the electromagnets and the targets do not meet these exacting specifications, the actual force produced by the E/I core actuator does not match the expected force calculated from the above equation. This inability to match the expected force and the actual force can cause limitations in the usage of E/I cores, and degrade overall system performance.
In light of the above, there is a need for a generalized E/I core commutation formula that compensates for the non-linearity of the E/I core force function and/or provides a linear transfer function between the input force command and actual EI force output. Further, there is a need for an E/I core commutation formula that compensates for the actual shape and alignment of the E/I cores. Additionally, there is a need for an EI commutation formula that minimizes the mismatch between the commutation and actual force function. Moreover, there is a need for an E/I core commutation formula that improves E/I core actuator performance and overall system performance.